Acetylene (C2 H2) and butane (C4 H10) are gaseous fuels with enthalpies of combustion of -49.9

Acetylene (C2 H2) and butane (C4 H10) are gaseous fuels with...

Acetylene $\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)$ and butane $\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)$ are gaseous fuels with enthalpies of combustion of $-49.9 \mathrm{~kJ} / \mathrm{g}$ and $-49.5 \mathrm{~kJ} / \mathrm{g}$, respectively. Compare the energy available from the combustion of a given volume of acetylene to the combustion energy from the same volume of butane at the same temperature and pressure.

Key Concepts

Enthalpy of Combustion

This concept refers to the energy released when a substance completely reacts with oxygen under standard conditions. It is often expressed on a per-mass or per-mole basis. In the context of fuels, the enthalpy of combustion indicates how much energy is produced per unit of fuel consumed during combustion, which is central when comparing the energetic performance of different fuels.

Molar Mass

Molar mass is the mass of one mole of a substance and is fundamental when converting energy values given per gram into energy per mole. Since combustion energies are sometimes provided on a per-mass basis, knowing the molar mass allows for the comparison of the energy output on a per-molecule or per-volume basis, particularly important when dealing with gaseous substances.

Ideal Gas Law

The ideal gas law (PV = nRT) establishes a relationship between the pressure, volume, temperature, and number of moles of a gas. Under constant temperature and pressure, the number of moles in a given volume is the same for all ideal gases. This principle is crucial when comparing the energy released per volume of different gaseous fuels because it ties the molecular properties of the gas to its volumetric energy density.

Energy Density

Energy density, in the context of fuels, refers to the amount of energy stored per unit volume or mass. When comparing fuels, especially in their gaseous form, assessing the energy available per unit volume is vital for practical applications. This involves considering both the enthalpy of combustion and the molar mass of the fuels, since equal volumes of gases at the same temperature and pressure contain equal numbers of moles.

Transcript

00:01 In this problem, we are asked to analyze, given a particular volume in temperature of these two particular gases.

00:11 We have a ceiling and butane gas, and we have their relative hates of combustion.

00:18 A ceiling which is marked a is 49.9 killed jules program.

00:23 And then the butane, which is b, is 49.5 killed rules program and i have their respective formulas on the right hand side.

00:31 So we're basically again asked to analyze if we're given a certain volume in a certain temperature for these gases, which we can pick any, um, scenarios that we like.

00:44 You know, how can we compare? ah, the heats of combustion given a certain volume and again a certain temperature.

00:52 So i went ahead and we'll start a new screen here.

00:55 So, um, i went ahead and picked one leader because that's convenient for calculations.

01:00 And 298 degrees kelvin is pretty much room temperature of 25 degrees celsius.

01:09 So if we would use pv equals in our tea, i can figure out how many moles of gas i have, and from there we can determine how much heat is release.

01:24 So we'll have to convert.

01:26 Aah! these constance here will have to convert those to a formal basis, you know, instead of ah uh, grams.

01:35 But if we go ahead and use it, i'll use one.

01:38 Atmosphere is at sea level.

01:39 Apus atmospheric pressure.

01:41 So we have one times one will have in our gas.

01:47 Constant is 0.8 to 1 and temperatures to 98.

01:54 No.

01:54 What? i divide equal sides by the product of our gas constant temperature.

01:59 I get end equals 0.0 for 09 moles.

02:07 Okay, so we have the same number moles of gas for each of these.

02:12 So if we go over the 1st 1 i went ahead and set it up.